Chapter 12, Problem 12.6A

Interpretation Introduction

(a)

Interpretation:

The formula of perovskite for a unit cell should be determined.

Concept introduction:

A unit cell is the smallest repeating unit of a crystal lattice. Unit cells are classified as primitive and non-primitive. Primitive unit cells are those which have atoms at only corners and non-primitive unit cells are those which have atoms at positions other than corners.

Non- primitive unit cells are of various types:

Face centered unit cell (fcc), body centered unit cell (bcc), edge centered unit cell, end centered unit cell.

Contribution of an atom at a position is as follows:

$\begin{array}{cc}\text{position in unit}\text{cell}& \text{contributions}\\ \text{center of body}& \text{1}\\ \text{center of face}& \text{1/2}\\ \text{center of edge}& \text{1/4}\\ \text{corners}& \text{1/8}\end{array}$

The number of particles per unit cell, also denoted by Z is as follows:

$\begin{array}{cc}\text{Unit}\text{cell}& Z\\ \text{scc}& \text{1}\\ \text{fcc}& \text{4}\\ \text{bcc}& \text{2}\\ \text{edge-centered}\text{cubic}& \text{4}\\ \text{end-centered}\text{cubic}& \text{2}\end{array}$

The elements or substances exist more in solid than liquid and gases. These solids can be two types amorphous and crystalline. The crystalline solids are solids that contain their constituent particle in arranged manner. While amorphous solids are solid in which constituent particles get arranged randomly such as rubber.

Interpretation Introduction

(b)

Interpretation:

The oxidation state of titanium ion of given perovskite unit cell should be determined.

Concept introduction:

The elements or substances exist more in solid than liquid and gases. These solids can be two types amorphous and crystalline. The crystalline solids are solids that contain their constituent particle in arranged manner. While amorphous solids are solid in which constituent particles get arranged randomly such as rubber.

Interpretation Introduction

(c)

Interpretation:

The geometry around each titanium, oxygen, and calcium atom in given unit cell should be determined.

Concept introduction:

The elements or substances exist more in solid than liquid and gases. These solids can be two types amorphous and crystalline. The crystalline solids are solids that contain their constituent particle in arranged manner. While amorphous solids are solid in which constituent particles get arranged randomly such as rubber.